@article{nguyen_tanizaki_unsal_2023, title={Study of gapped phases of 4d gauge theories using temporal gauging of the Z(N) 1-form symmetry}, ISSN={["1029-8479"]}, DOI={10.1007/JHEP08(2023)013}, abstractNote={Abstract
To study gapped phases of 4d gauge theories, we introduce the temporal gauging of ℤN 1-form symmetry in 4d quantum field theories (QFTs), thereby defining effective 3d QFTs with $$ \overset{\sim }{\mathbb{Z}} $$
ℤ
~
N × ℤN 1-form symmetry. In this way, spatial fundamental Wilson and ’t Hooft loops are simultaneously genuine line operators. Assuming a mass gap and Lorentz invariant vacuum of the 4d QFT, the $$ \overset{\sim }{\mathbb{Z}} $$
ℤ
~
N × ℤN symmetry must be spontaneously broken to an order-N subgroup H, and we can classify the 4d gapped phases by specifying H. This establishes the 1-to-1 correspondence between the two classification schemes for gapped phases of 4d gauge theories: one is the conventional Wilson-’t Hooft classification, and the other is the modern classification using the spontaneous breaking of 4d 1-form symmetry enriched with symmetry-protected topological states.}, number={8}, journal={JOURNAL OF HIGH ENERGY PHYSICS}, author={Nguyen, Mendel and Tanizaki, Yuya and Unsal, Mithat}, year={2023}, month={Aug} }
@article{nguyen_tanizaki_unsal_2023, title={Winding ? and destructive interference of instantons}, ISSN={["1029-8479"]}, DOI={10.1007/JHEP09(2023)033}, abstractNote={A bstract While the θ dependence of field theories is 2 π periodic, the ground-state wavefunctions at θ and θ + 2 π often belong to different classes of symmetry-protected topological states. When this is the case, a continuous change of the θ parameter can introduce an interface that supports a nontrivial field theory localized on the wall. We consider the 2d ℂ P N −1 sigma model as an example and construct a weak-coupling setup of this interface theory by considering the small S 1 compactification with nonzero winding θ parameter and a suitable symmetry-twisted boundary condition. This system has N classical vacua connected by fractional instantons, but the anomaly constraint tells us that the fractional-instanton amplitudes should vanish completely to have N -fold degeneracy at the quantum level. We show how this happens in this purely bosonic system, uncovering that the integration over the zero modes annihilates the fractional instanton amplitudes, in sharp contrast to what happens when the θ angle is constant. Moreover, we provide another explanation of this selection rule by showing that the N perturbative vacua acquire different charges under the global symmetry with the activation of the winding θ angle. We also demonstrate a similar destructive interference between instanton effects in the ℂ P N −1 quantum mechanics with the Berry phase.}, number={9}, journal={JOURNAL OF HIGH ENERGY PHYSICS}, author={Nguyen, Mendel and Tanizaki, Yuya and Unsal, Mithat}, year={2023}, month={Sep} }
@article{tanizaki_unsal_2022, title={Center vortex and confinement in Yang Mills theory and QCD with anomaly-preserving compactifications}, volume={2022}, ISSN={["2050-3911"]}, url={http://dx.doi.org/10.1093/ptep/ptac042}, DOI={10.1093/ptep/ptac042}, abstractNote={Abstract
We construct an anomaly-preserving compactification of 4D gauge theories, including SU(N) Yang–Mills theory, $\mathcal {N}=1$ supersymmetric Yang–Mills theory, and quantum chromodynamics (QCD), down to 2D by turning on the ’t Hooft flux through T2. This provides a new framework to analytically calculate nonperturbative properties such as confinement, chiral symmetry breaking, and the multi-branch structure of vacua. We give a semiclassical description of these phenomena based on the center vortex and show that it enjoys the same anomaly-matching condition as the original 4D gauge theory. We conjecture that the weak-coupling vacuum structure on small $T^2 \times \mathbb {R}^2$ is adiabatically connected to the strong-coupling regime on $\mathbb {R}^4$ without any phase transitions. In QCD with fundamental quarks as well, we can turn on the ’t Hooft flux either by activating the SU(Nf)V symmetry twist for Nf = N flavors or by introducing a magnetic flux of baryon number U(1)B for arbitrary Nf flavors. In both cases, the weak-coupling center-vortex theory gives a prediction consistent with the chiral Lagrangian of 4D QCD.}, number={4}, journal={PROGRESS OF THEORETICAL AND EXPERIMENTAL PHYSICS}, publisher={Oxford University Press (OUP)}, author={Tanizaki, Yuya and Unsal, Mithat}, year={2022}, month={Apr} }
@article{honda_itou_tanizaki_2022, title={DMRG study of the higher-charge Schwinger model and its ’t Hooft anomaly}, volume={11}, url={http://inspirehep.net/record/2163166}, DOI={10.1007/JHEP11(2022)141}, abstractNote={Abstract
The charge-q Schwinger model is the (1 + 1)-dimensional quantum electrodynamics (QED) with a charge-q Dirac fermion. It has the ℤq 1-form symmetry and also enjoys the ℤq chiral symmetry in the chiral limit, and there is a mixed ’t Hooft anomaly between those symmetries. We numerically study the charge-q Schwinger model in the lattice Hamiltonian formulation using the density-matrix renormalization group (DMRG). When applying DMRG, we map the Schwinger model to a spin chain with nonlocal interaction via Jordan-Wigner transformation, and we take the open boundary condition instead of the periodic one to make the Hilbert space finite-dimensional. When computing the energy density or chiral condensate, we find that using local operators significantly reduces the boundary effect compared with the computation of corresponding extensive quantities divided by the volume. To discuss the consequence of the ’t Hooft anomaly, we carefully treat the renormalization of the chiral condensates, and then we confirm that Wilson loops generate the discrete chiral transformations in the continuum limit.}, journal={JHEP}, author={Honda, Masazumi and Itou, Etsuko and Tanizaki, Yuya}, year={2022}, month={Nov}, pages={141} }
@article{fukushima_shimazaki_tanizaki_2022, title={Exploring the θ-vacuum structure in the functional renormalization group approach}, volume={04}, url={http://inspirehep.net/record/2023555}, DOI={10.1007/JHEP04(2022)040}, abstractNote={Abstract
We investigate the θ-vacuum structure and the ’t Hooft anomaly at θ = π in a simple quantum mechanical system on S1 to scrutinize the applicability of the functional renormalization group (fRG) approach. Even though the fRG is an exact formulation, a naive application of the fRG equation would miss contributions from the θ term due to the differential nature of the formulation. We first review this quantum mechanical system on S1 that is solvable with both the path integral and the canonical quantization. We discuss how to construct the quantum effective action including the θ dependence. Such an explicit calculation poses a subtle question of whether a Legendre transform is well defined or not for general systems with the sign problem. We then consider a deformed theory to relax the integral winding by introducing a wine-bottle potential with the finite depth ∝ g, so that the original S1 theory is recovered in the g → ∞ limit. We numerically solve the energy spectrum in the deformed theory as a function of g and θ in the canonical quantization. We test the efficacy of the simplest local potential approximation (LPA) in the fRG approach and find that the correct behavior of the ground state energy is well reproduced for small θ. When the energy level crossing is approached, the LPA flow breaks down and fails in describing the ground state degeneracy expected from the ’t Hooft anomaly. We finally turn back to the original theory and discuss an alternative formulation using the Villain lattice action. The analysis with the Villain lattice at θ = π indicates that the nonlocality of the effective action is crucial to capture the level crossing behavior of the ground states.}, journal={JHEP}, author={Fukushima, Kenji and Shimazaki, Takuya and Tanizaki, Yuya}, year={2022}, month={Apr}, pages={040} }
@article{hayashi_tanizaki_2022, title={Non-invertible self-duality defects of Cardy-Rabinovici model and mixed gravitational anomaly}, volume={2022}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85135228761&partnerID=MN8TOARS}, DOI={10.1007/JHEP08(2022)036}, abstractNote={Abstract
We study properties of self-duality symmetry in the Cardy-Rabinovici model. The Cardy-Rabinovici model is the 4d U(1) gauge theory with electric and magnetic matters, and it enjoys the SL(2, ℤ) self-duality at low-energies. SL(2, ℤ) self-duality does not realize in a naive way, but we notice that the STp duality transformation becomes the legitimate duality operation by performing the gauging of ℤN 1-form symmetry with including the level-p discrete topological term. Due to such complications in its realization, the fusion rule of duality defects becomes a non-group-like structure, and thus the self-duality symmetry is realized as a non-invertible symmetry. Moreover, for some fixed points of the self-duality, the duality symmetry turns out to have a mixed gravitational anomaly detected on a K3 surface, and we can rule out the trivially gapped phase as a consequence of anomaly matching. We also uncover how the conjectured phase diagram of the Cardy-Rabinovici model satisfies this new anomaly matching condition.}, number={8}, journal={Journal of High Energy Physics}, author={Hayashi, Y. and Tanizaki, Y.}, year={2022} }
@article{tanizaki_unsal_2022, title={Semiclassics with 't Hooft flux background for QCD with 2-index quarks}, volume={08}, ISSN={["1029-8479"]}, url={http://inspirehep.net/record/2086495}, DOI={10.1007/JHEP08(2022)038}, abstractNote={Abstract
We study quantum chromodynamics including the two-index symmetric or anti-symmetric quark (QCD(Sym/ASym)) on small ℝ2× T2 with a suitable magnetic flux. We first discuss the ’t Hooft anomaly of these theories and claim that discrete chiral symmetry should be spontaneously broken completely to satisfy the anomaly matching condition. The T2 compactification with the magnetic flux preserves the ’t Hooft anomaly, and the 2d effective theory is constrained by the same anomaly of 4d QCD(Sym/ASym). We demonstrate the spontaneous breakdown of chiral symmetry using the dilute gas of center vortices, which confirms the prediction of the ’t Hooft anomaly. We also find that each vacuum maintains the charge conjugation symmetry, and this gives affirmative support for the nonperturbative large-N orientifold equivalence between QCD(Sym/ASym) and $$ \mathcal{N} $$
N
= 1 supersymmetric SU(N) Yang-Mills theory.}, number={8}, journal={JOURNAL OF HIGH ENERGY PHYSICS}, author={Tanizaki, Yuya and Unsal, Mithat}, year={2022}, month={Aug} }
@article{honda_itou_kikuchi_tanizaki_2021, title={Negative string tension of higher-charge Schwinger model via digital quantum simulation}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85118645604&partnerID=MN8TOARS}, journal={arXiv}, author={Honda, M. and Itou, E. and Kikuchi, Y. and Tanizaki, Y.}, year={2021} }
@article{nguyen_tanizaki_ünsal_2021, title={Non-invertible 1-form symmetry and Casimir scaling in 2d Yang-Mills theory}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85106167565&partnerID=MN8TOARS}, journal={arXiv}, author={Nguyen, M. and Tanizaki, Y. and Ünsal, M.}, year={2021} }
@article{nguyen_tanizaki_unsal_2021, title={Noninvertible 1-form symmetry and Casimir scaling in 2D Yang-Mills theory}, volume={104}, ISSN={["2470-0029"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85114421307&partnerID=MN8TOARS}, DOI={10.1103/PhysRevD.104.065003}, abstractNote={Pure Yang-Mills theory in 2 spacetime dimensions shows exact Casimir scaling. Thus there are infinitely many string tensions, and this has been understood as a result of non-propagating gluons in 2 dimensions. From ordinary symmetry considerations, however, this richness in the spectrum of string tensions seems mysterious. Conventional wisdom has it that it is the center symmetry that classifies string tensions, but being finite it cannot explain infinitely many confining strings. In this note, we resolve this discrepancy between dynamics and kinematics by pointing out the existence of a non-invertible 1-form symmetry, which is able to distinguish Wilson loops in different representations. We speculate on possible implications for Yang-Mills theories in 3 and 4 dimensions.}, number={6}, journal={PHYSICAL REVIEW D}, author={Nguyen, Mendel and Tanizaki, Yuya and Unsal, Mithat}, year={2021}, month={Sep} }
@article{nguyen_tanizaki_ünsal_2021, title={Semi-Abelian gauge theories, non-invertible symmetries, and string tensions beyond $N$-ality}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85101229833&partnerID=MN8TOARS}, journal={arXiv}, author={Nguyen, M. and Tanizaki, Y. and Ünsal, M.}, year={2021} }
@article{nguyen_tanizaki_unsal_2021, title={Semi-Abelian gauge theories, non-invertible symmetries, and string tensions beyond N-ality}, volume={03}, ISSN={["1029-8479"]}, url={http://inspirehep.net/record/1839639}, DOI={10.1007/JHEP03(2021)238}, abstractNote={Abstract
We study a 3d lattice gauge theory with gauge group U(1)N−1 ⋊ SN, which is obtained by gauging the SN global symmetry of a pure U(1)N−1 gauge theory, and we call it the semi-Abelian gauge theory. We compute mass gaps and string tensions for both theories using the monopole-gas description. We find that the effective potential receives equal contributions at leading order from monopoles associated with the entire SU(N) root system. Even though the center symmetry of the semi-Abelian gauge theory is given by ℤN, we observe that the string tensions do not obey the N-ality rule and carry more detailed information on the representations of the gauge group. We find that this refinement is due to the presence of non-invertible topological lines as a remnant of U(1)N−1 one-form symmetry in the original Abelian lattice theory. Upon adding charged particles corresponding to W-bosons, such non-invertible symmetries are explicitly broken so that the N-ality rule should emerge in the deep infrared regime.}, number={3}, journal={JOURNAL OF HIGH ENERGY PHYSICS}, author={Nguyen, Mendel and Tanizaki, Yuya and Unsal, Mithat}, year={2021}, month={Mar} }
@article{takahashi_tanizaki_2021, title={Sigma-model analysis of SU(3) antiferromagnetic spins on the triangular lattice}, volume={104}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85122103042&partnerID=MN8TOARS}, DOI={10.1103/PhysRevB.104.235152}, abstractNote={Using field-theoretic techniques, we study the $SU(3)$ analogue of anti-ferromagnetic Heisenberg spin model on the triangular lattice putting the $p$-box symmetric representation on each site. Taking the large-$p$ limit, we show that the low-energy effective theory is described by a $(2+1)$-dimensional relativistic $SU(3)/U(1)^2$ nonlinear sigma model. Since the target space has a nontrivial homotopy $\pi_2(SU(3)/U(1)^2)\simeq \mathbb{Z}^2$, this model has two kinds of magnetic skyrmions, which can be created and annihilated by monopole instantons. By careful analysis of the Wess-Zumino term in the spin coherent path integral, we compute the Berry phase for these monopoles and it produces the destructive interference. This restricts possible perturbations of the effective Lagrangian by monopole operators, and we see that the valence-bond-solid (VBS) phase should have degenerate ground states when $p\not\in 3\mathbb{Z}$. We also compute 't Hooft anomalies to constrain possible phases of this system, and a direct phase transition between N\'eel and VBS phases is supported from the anomaly matching.}, number={23}, journal={Physical Review B}, author={Takahashi, I. and Tanizaki, Y.}, year={2021} }
@article{takahashi_tanizaki_2021, title={Sigma-model analysis of SU(3) antiferromagnetic spins on the triangular lattice}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85115844171&partnerID=MN8TOARS}, journal={arXiv}, author={Takahashi, I. and Tanizaki, Y.}, year={2021} }
@article{kobayashi_lee_shiozaki_tanizaki_2021, title={Topological terms of (2+1)d flag-manifold sigma models}, volume={2021}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85112854890&partnerID=MN8TOARS}, DOI={10.1007/JHEP08(2021)075}, abstractNote={Abstract
We examine topological terms of (2 + 1)d sigma models and their consequences in the light of classifications of invertible quantum field theories utilizing bordism groups. In particular, we study the possible topological terms for the U(N)/U(1)N flag-manifold sigma model in detail. We argue that the Hopf-like term is absent, contrary to the expectation from a nontrivial homotopy group π3(U(N)/U(1)N) = ℤ, and thus skyrmions cannot become anyons with arbitrary statistics. Instead, we find that there exist $$ \frac{N\left(N-1\right)}{2}-1 $$
N
N
−
1
2
−
1
types of Chern-Simons terms, some of which can turn skyrmions into fermions, and we write down explicit forms of effective Lagrangians.}, number={8}, journal={Journal of High Energy Physics}, author={Kobayashi, Ryohei and Lee, Yasunori and Shiozaki, Ken and Tanizaki, Yuya}, year={2021}, pages={075} }
@article{kobayashi_lee_shiozaki_tanizaki_2021, title={Topological terms of (2+1)d flag-manifold sigma models}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85103025056&partnerID=MN8TOARS}, journal={arXiv}, author={Kobayashi, R. and Lee, Y. and Shiozaki, K. and Tanizaki, Y.}, year={2021} }
@article{cherman_jacobson_tanizaki_ünsal_2020, title={Anomalies, a mod 2 index, and dynamics of 2d adjoint QCD}, volume={8}, url={http://inspirehep.net/record/1751322}, DOI={10.21468/SciPostPhys.8.5.072}, abstractNote={We show that 22d
adjoint QCD, an SU(N)SU(N)
gauge theory with one massless adjoint Majorana fermion, has a variety
of mixed ’t Hooft anomalies. The anomalies are derived using a recent
mod 22
index theorem and its generalization that incorporates ’t Hooft flux.
Anomaly matching and dynamical considerations are used to determine the
ground-state structure of the theory. The anomalies, which are present
for most values of NN,
are matched by spontaneous chiral symmetry breaking. We find that
massless 22d
adjoint QCD confines for N >2N>2,
except for test charges of NN-ality
N/2N/2,
which are deconfined. In other words, \mathbb Z_NℤN
center symmetry is unbroken for odd NN
and spontaneously broken to \mathbb Z_{N/2}ℤN/2
for even NN.
All of these results are confirmed by explicit calculations on small
\mathbb{R}\times S^1ℝ×S1.
We also show that this non-supersymmetric theory exhibits exact
Bose-Fermi degeneracies for all states, including the vacua, when
NN
is even. Furthermore, for most values of NN,
22d
massive adjoint QCD describes a non-trivial symmetry-protected
topological (SPT) phase of matter, including certain cases where the
number of interacting Majorana fermions is a multiple of
88.
As a result, it fits into the classification of
(1+1)(1+1)d
SPT phases of interacting Majorana fermions in an interesting way.}, number={5}, journal={SciPost Phys.}, author={Cherman, Aleksey and Jacobson, Theodore and Tanizaki, Yuya and Ünsal, Mithat}, year={2020}, month={May}, pages={072} }
@article{chen_fukushima_nishimura_tanizaki_2020, title={Deconfinement and CP breaking at θ=π in Yang-Mills theories and a novel phase for SU(2)}, volume={102}, url={http://inspirehep.net/record/1798942}, DOI={10.1103/physrevd.102.034020}, abstractNote={We discuss the deconfinement and the CP-breaking phase transitions at $\theta=\pi$ in Yang-Mills theories. The 't Hooft anomaly matching prohibits the confined phase with CP symmetry and requires $T_{dec}(\theta=\pi) \le T_{CP}$, where $T_{dec}(\theta=\pi)$ and $T_{CP}$ denote the deconfinement and the CP-restoration temperatures, respectively, at $\theta=\pi$. We analytically study these two phase transitions in softly-broken $\mathcal{N}=1$ supersymmetric Yang-Mills theories on small $\mathbb{R}^3\times S^1$ with the periodic boundary condition for gluinos. For most gauge groups except SU(2) in this model, we find that the inequality is saturated, so deconfinement and CP restoration occur simultaneously. We demonstrate special features of the SU(2) gauge theory: There is a finite window of two temperatures, $T_{dec}(\pi)2 flag sigma model on ℝ × S^{1}}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85094513756&partnerID=MN8TOARS}, journal={arXiv}, author={Hongo, M. and Misumi, T. and Tanizaki, Y.}, year={2018} }
@article{dunne_tanizaki_unsal_2018, title={Quantum distillation of Hilbert spaces, semi-classics and anomaly matching}, volume={08}, ISSN={["1029-8479"]}, url={http://inspirehep.net/record/1658917}, DOI={10.1007/JHEP08(2018)068}, abstractNote={Abstract
A symmetry-twisted boundary condition of the path integral provides a suitable framework for the semi-classical analysis of nonperturbative quantum field theories (QFTs), and we reinterpret it from the viewpoint of the Hilbert space. An appropriate twist with the unbroken symmetry can potentially produce huge cancellations among excited states in the state-sum, without affecting the ground states; we call this effect “quantum distillation”. Quantum distillation can provide the underlying mechanism for adiabatic continuity, by preventing a phase transition under S
1 compactification. We revisit this point via the ’t Hooft anomaly matching condition when it constrains the vacuum structure of the theory on ℝ
d
and upon compactification. We show that there is a precise relation between the persistence of the anomaly upon compactification, the Hilbert space quantum distillation, and the semi-classical analysis of the corresponding symmetry-twisted path integrals. We motivate quantum distillation in quantum mechanical examples, and then study its non-trivial action in QFT, with the example of the 2D Grassmannian sigma model Gr(N, M). We also discuss the connection of quantum distillation with large-N volume independence and flavor-momentum transmutation.}, number={8}, journal={JOURNAL OF HIGH ENERGY PHYSICS}, author={Dunne, Gerald V. and Tanizaki, Yuya and Unsal, Mithat}, year={2018}, month={Aug} }
@article{dunne_tanizaki_unsal_2018, title={Quantum distillation of Hilbert spaces, semi-classics and anomaly matching}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85093588857&partnerID=MN8TOARS}, journal={arXiv}, author={Dunne, G.V. and Tanizaki, Y. and Unsal, M.}, year={2018} }
@article{hirono_tanizaki_2018, title={Quark-hadron continuity beyond Ginzburg-Landau paradigm}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85094511557&partnerID=MN8TOARS}, journal={arXiv}, author={Hirono, Y. and Tanizaki, Y.}, year={2018} }
@article{tanizaki_misumi_sakai_2017, title={Circle compactification and 't Hooft anomaly}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85094235087&partnerID=MN8TOARS}, journal={arXiv}, author={Tanizaki, Y. and Misumi, T. and Sakai, N.}, year={2017} }
@article{tanizaki_misumi_sakai_2017, title={Circle compactification and ’t Hooft anomaly}, volume={12}, url={http://inspirehep.net/record/1632455}, DOI={10.1007/JHEP12(2017)056}, abstractNote={Anomaly matching constrains low-energy physics of strongly-coupled field theories, but it is not useful at finite temperature due to contamination from high-energy states. The known exception is an 't Hooft anomaly involving one-form symmetries as in pure $SU(N)$ Yang-Mills theory at $\theta=\pi$. Recent development about large-$N$ volume independence, however, gives us a circumstantial evidence that 't Hooft anomalies can also remain under circle compactifications in some theories without one-form symmetries. We develop a systematic procedure for deriving an 't Hooft anomaly of the circle-compactified theory starting from the anomaly of the original uncompactified theory without one-form symmetries, where the twisted boundary condition for the compactified direction plays a pivotal role. As an application, we consider $\mathbb{Z}_N$-twisted $\mathbb{C}P^{N-1}$ sigma model and massless $\mathbb{Z}_N$-QCD, and compute their anomalies explicitly.}, number={12}, journal={JHEP}, author={Tanizaki, Yuya and Misumi, Tatsuhiro and Sakai, Norisuke}, year={2017}, month={Dec}, pages={056} }
@article{kikuchi_tanizaki_2017, title={Global inconsistency, 't Hooft anomaly, and level crossing in quantum mechanics}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85093463966&partnerID=MN8TOARS}, journal={arXiv}, author={Kikuchi, Y. and Tanizaki, Y.}, year={2017} }
@article{kikuchi_tanizaki_2017, title={Global inconsistency, ’t Hooft anomaly, and level crossing in quantum mechanics}, volume={2017}, url={http://inspirehep.net/record/1614649}, DOI={10.1093/ptep/ptx148}, abstractNote={An 't Hooft anomaly is the obstruction for gauging symmetries, and it constrains possible low-energy behaviors of quantum field theories by excluding trivial infrared theories. Global inconsistency condition is recently proposed as a milder condition but is expected to play an almost same role by comparing high symmetry points in the theory space. In order to clarify the consequence coming from this new condition, we discuss several quantum mechanical models with topological angles and explicitly compute their energy spectra. It turns out that the global inconsistency can be saturated not only by the ground-state degeneracy at either of high symmetry points but also by the level crossing (phase transition) separating those high symmetry points.}, number={11}, journal={PTEP}, author={Kikuchi, Yuta and Tanizaki, Yuya}, year={2017}, month={Nov}, pages={113B05} }
@article{tanizaki_nishimura_verbaarschot_2017, title={Gradient flows without blow-up for Lefschetz thimbles}, volume={10}, url={http://inspirehep.net/record/1604895}, DOI={10.1007/JHEP10(2017)100}, abstractNote={We propose new gradient flows that define Lefschetz thimbles and do not blow up in a finite flow time. We study analytic properties of these gradient flows, and confirm them by numerical tests in simple examples.}, number={10}, journal={JHEP}, author={Tanizaki, Yuya and Nishimura, Hiromichi and Verbaarschot, Jacobus J.M.}, year={2017}, month={Oct}, pages={100} }
@article{tanizaki_nishimura_verbaarschot_2017, title={Gradient flows without blow-up for Lefschetz thimbles}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85093307885&partnerID=MN8TOARS}, journal={arXiv}, author={Tanizaki, Y. and Nishimura, H. and Verbaarschot, J.J.M.}, year={2017} }
@inproceedings{tanizaki_hidaka_hayata_2016, place={Southampton, United Kingdom}, title={Lefschetz-thimble approach to the Silver Blaze problem of one-site fermion model}, volume={LATTICE2016}, url={http://inspirehep.net/record/1489199}, DOI={10.22323/1.256.0030}, abstractNote={The sign problem of finite-density QCD at the zero temperature becomes very severe if the quark chemical potential exceeds half of the pion mass. In order to understand its property, we consider the sign problem of the one-site fermion model appearing in its path-integral expression by using the Lefschetz-thimble method. We show that the original integration cycle becomes decomposed into multiple Lefschetz thimbles at a certain value of the fermion chemical potential, which would correspond to half of the pion mass of finite-density QCD. This triggers a fictitious phase transition on each Lefschetz thimble, and the interference of complex phases among them plays an important role for the correct description of the system. We also show that the complex Langevin method does not work in this situation.}, booktitle={PoS}, publisher={SISSA}, author={Tanizaki, Yuya and Hidaka, Yoshimasa and Hayata, Tomoya}, year={2016}, month={Sep}, pages={030} }
@article{tanizaki_hatsuda_2017, title={Multi-Regulator Functional Renormalization Group for Many-Fermion Systems}, volume={26}, url={http://inspirehep.net/record/1279937}, DOI={10.1142/S0218301317400274}, abstractNote={ We propose a method of multi-regulator functional renormalization group (MR-FRG) which is a novel formulation of functional renormalization group with multiple infrared (IR) regulators. It is applied to a two-component fermionic system with an attractive contact interaction to study crossover phenomena between the Bardeen–Cooper–Schrieffer (BCS) phase and the Bose–Einstein condensation (BEC) phase. To control both the fermionic one-particle excitations and the bosonic collective excitations, IR regulators are introduced, one for the fermionic two-point function and another for the four-fermion vertex. It is shown that the Nozières–Schmitt-Rink (NSR) theory, which is successful to capture qualitative features of the BCS–BEC crossover, can be derived from MR–FRG. Some aspects of MR-FRG to go beyond the NSR theory are also discussed. }, number={01n02}, journal={Int.J.Mod.Phys.E}, author={Tanizaki, Yuya and Hatsuda, Tetsuo}, year={2017}, month={Jan}, pages={1740027} }
@article{tanizaki_tachibana_2017, title={Multi-flavor massless QED$_2$ at finite densities via Lefschetz thimbles}, volume={02}, url={http://inspirehep.net/record/1505181}, DOI={10.1007/JHEP02(2017)081}, abstractNote={We consider multi-flavor massless (1 + 1)-dimensional QED with chemical potentials at finite spatial length and the zero-temperature limit. Its sign problem is solved using the mean-field calculation with complex saddle points.}, number={2}, journal={JHEP}, author={Tanizaki, Yuya and Tachibana, Motoi}, year={2017}, month={Feb}, pages={081} }
@article{hayata_kikuchi_tanizaki_2017, title={Topological Properties of the Chiral Magnetic Effect in Multi-Weyl Semimetals}, volume={96}, url={http://inspirehep.net/record/1516418}, DOI={10.1103/PhysRevB.96.085112}, abstractNote={We compute the chiral magnetic effect (CME) in multi-Weyl semimetals (multi-WSMs) based on the chiral kinetic theory. Multi-WSMs are WSMs with multiple monopole charges that have nonlinear and anisotropic dispersion relations near the Weyl points, and we need to extend the conventional computation of the CME in WSMs with linear dispersion relations. The topological properties of the CME in multi-WSMs are investigated in detail for not only static magnetic fields but also time-dependent (dynamic) ones. We propose an experimental setup to measure the multiple monopole charge via the topological nature hidden in the dynamic CME.}, number={8}, journal={Phys.Rev.B}, author={Hayata, Tomoya and Kikuchi, Yuta and Tanizaki, Yuya}, year={2017}, month={Aug}, pages={085112} }
@article{hayata_kikuchi_tanizaki_2017, title={Topological properties of the chiral magnetic effect in multi-Weyl semimetals}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85093248678&partnerID=MN8TOARS}, journal={arXiv}, author={Hayata, T. and Kikuchi, Y. and Tanizaki, Y.}, year={2017} }
@article{tanizaki_kikuchi_2017, title={Vacuum structure of bifundamental gauge theories at finite topological angles}, volume={06}, url={http://inspirehep.net/record/1598267}, DOI={10.1007/JHEP06(2017)102}, abstractNote={We discuss possible vacuum structures of $SU(n)\times SU(n)$ gauge theories with bifundamental matters at finite $\theta$ angles. In order to give a precise constraint, a mixed 't Hooft anomaly is studied in detail by gauging the center $\mathbb{Z}_n$ one-form symmetry of the bifundamental gauge theory. We propose phase diagrams that are consistent with the constraints, and also give a heuristic explanation of the result based on the dual superconductor scenario of confinement.}, number={6}, journal={JHEP}, author={Tanizaki, Yuya and Kikuchi, Yuta}, year={2017}, month={Jun}, pages={102} }
@article{tanizaki_kikuchi_2017, title={Vacuum structure of bifundamental gauge theories at finite topological angles}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85093405522&partnerID=MN8TOARS}, journal={arXiv}, author={Tanizaki, Y. and Kikuchi, Y.}, year={2017} }
@article{hayata_hidaka_tanizaki_2016, title={Complex saddle points and the sign problem in complex Langevin simulation}, volume={911}, url={http://inspirehep.net/record/1403563}, DOI={10.1016/j.nuclphysb.2016.07.031}, abstractNote={We show that complex Langevin simulation converges to a wrong result within the semiclassical analysis, by relating it to the Lefschetz-thimble path integral, when the path-integral weight has different phases among dominant complex saddle points. Equilibrium solution of the complex Langevin equation forms local distributions around complex saddle points. Its ensemble average approximately becomes a direct sum of the average in each local distribution, where relative phases among them are dropped. We propose that by taking these phases into account through reweighting, we can solve the wrong convergence problem. However, this prescription may lead to a recurrence of the sign problem in the complex Langevin method for quantum many-body systems.}, journal={Nucl.Phys.B}, author={Hayata, Tomoya and Hidaka, Yoshimasa and Tanizaki, Yuya}, year={2016}, month={Oct}, pages={94–105} }
@article{tanizaki_hidaka_hayata_2016, title={Lefschetz-thimble analysis of the sign problem in one-site fermion model}, volume={18}, url={http://inspirehep.net/record/1394683}, DOI={10.1088/1367-2630/18/3/033002}, abstractNote={The Lefschetz-thimble approach to path integrals is applied to a one-site model of electrons, i.e., the one-site Hubbard model. Since the one-site Hubbard model shows a non-analytic behavior at the zero temperature and its path integral expression has the sign problem, this toy model is a good testing ground for an idea or a technique to attack the sign problem. Semiclassical analysis using complex saddle points unveils the significance of interference among multiple Lefschetz thimbles to reproduce the non-analytic behavior by using the path integral. If the number of Lefschetz thimbles is insufficient, we found not only large discrepancies from the exact result, but also thermodynamic instabilities. Analyzing such singular behaviors semiclassically, we propose a criterion to identify the necessary number of Lefschetz thimbles. We argue that this interference of multiple saddle points is a key issue to understand the sign problem of the finite-density quantum chromodynamics.}, number={3}, journal={New J.Phys.}, publisher={IOP Publishing}, author={Tanizaki, Yuya and Hidaka, Yoshimasa and Hayata, Tomoya}, year={2016}, month={Mar}, pages={033002} }
@inproceedings{tanizaki_nishimura_kashiwa_2015, place={Kobe, Japan}, title={Lefschetz-thimble path integral for solving the mean-field sign problem}, volume={LATTICE2015}, url={http://inspirehep.net/record/1476940}, DOI={10.22323/1.251.0282}, abstractNote={The sign problem is a serious obstacle not only for the Monte Carlo method in lattice field theories, but also for the mean-field approximation in the effective models.The Lefschetz-thimble approach can be a key clue to understand these problems, and we show that the mean-field sign problem can be solved.}, booktitle={PoS}, publisher={SISSA}, author={Tanizaki, Yuya and Nishimura, Hiromichi and Kashiwa, Kouji}, year={2015}, month={Aug}, pages={282} }
@article{tanizaki_nishimura_kashiwa_2015, title={Evading the sign problem in the mean-field approximation through Lefschetz-thimble path integral}, volume={91}, url={http://inspirehep.net/record/1359295}, DOI={10.1103/PhysRevD.91.101701}, abstractNote={The fermion sign problem appearing in the mean-field approximation is considered, and the systematic computational scheme of the free energy is devised by using the Lefschetz-thimble method. We show that the Lefschetz-thimble method respects the reflection symmetry, which makes physical quantities manifestly real at any order of approximations using complex saddle points. The formula is demonstrated through the Airy integral as an example, and its application to the Polyakov-loop effective model of dense QCD is discussed in detail.}, number={10}, journal={Phys.Rev.D}, publisher={American Physical Society (APS)}, author={Tanizaki, Yuya and Nishimura, Hiromichi and Kashiwa, Kouji}, year={2015}, month={May}, pages={101701} }
@article{mesterhazy_stockemer_tanizaki_2015, title={From quantum to classical dynamics: The relativistic $O(N)$ model in the framework of the real-time functional renormalization group}, volume={92}, url={http://inspirehep.net/record/1365098}, DOI={10.1103/PhysRevD.92.076001}, abstractNote={We investigate the transition from unitary to dissipative dynamics in the relativistic O(N) vector model with the λ(φ2)2 interaction using the nonperturbative functional renormalization group in the real-time formalism. In thermal equilibrium, the theory is characterized by two scales, the interaction range for coherent scattering of particles and the mean free path determined by the rate of incoherent collisions with excitations in the thermal medium. Their competition determines the renormalization group flow and the effective dynamics of the model. Here we quantify the dynamic properties of the model in terms of the scale-dependent dynamic critical exponent z in the limit of large temperatures and in 2≤d≤4 spatial dimensions. We contrast our results to the behavior expected at vanishing temperature and address the question of the appropriate dynamic universality class for the given microscopic theory.}, number={7}, journal={Phys.Rev.D}, author={Mesterhazy, David and Stockemer, Jan H. and Tanizaki, Yuya}, year={2015}, month={Oct}, pages={076001} }
@unpublished{mesterházy_stockemer_tanizaki_2015, title={From quantum to classical dynamics: The relativistic O(N) model in the framework of the real-time functional renormalization group}, url={http://inspirehep.net/record/1365098}, author={Mesterházy, David and Stockemer, Jan H. and Tanizaki, Yuya}, year={2015}, month={Apr} }
@article{fukushima_tanizaki_2015, title={Hamilton dynamics for Lefschetz-thimble integration akin to the complex Langevin method}, volume={2015}, url={http://inspirehep.net/record/1385114}, DOI={10.1093/ptep/ptv152}, abstractNote={1. Introduction. The rst-principle approach to solve the theory is an ultimate goal of theoretical investigations. The quantum Monte Carlo simulation for the functional integral has been a powerful ab initio technique to reveal non-perturbative features of various phys- ical systems. Successful applications include the lattice-QCD (Quantum Chromodynamics) simulation, the lattice Hubbard model, the path integral representation of spin systems, etc. The Monte-Carlo algorithm is based on importance sampling, so it is demanded that the integrand should be positive semi-denite, i.e., e}, number={11}, journal={PTEP}, author={Fukushima, Kenji and Tanizaki, Yuya}, year={2015}, month={Nov}, pages={111A01} }
@article{tanizaki_2015, title={Lefschetz-thimble techniques for path integral of zero-dimensional O (n) sigma models}, volume={91}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84922570057&partnerID=MN8TOARS}, DOI={10.1103/PhysRevD.91.036002}, abstractNote={Zero-dimensional $O(n)$-symmetric sigma models are studied by using Picard--Lefschetz integration method in the presence of small symmetry-breaking perturbations. Due to approximate symmetry, downward flows turn out to show significant structures: They slowly travel along the set of pseudo classical points, and branch into other directions so as to span middle-dimensional integration cycles. We propose an efficient way to find such slow motions for computing Lefschetz thimbles. In the limit of symmetry restoration, we figure out that only special combinations of Lefschetz thimbles can survive as convergent integration cycles: Other integrations become divergent due to non-compactness of the complexified group of symmetry. We also compute downward flows of $O(2)$-symmetric fermionic systems, and confirm that all of these properties are true also with fermions.}, number={3}, journal={Phys. Rev. D}, publisher={American Physical Society (APS)}, author={Tanizaki, Yuya}, year={2015}, pages={036002} }
@article{kanazawa_tanizaki_2015, title={Structure of Lefschetz thimbles in simple fermionic systems}, volume={2015}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84924873080&partnerID=MN8TOARS}, DOI={10.1007/JHEP03(2015)044}, abstractNote={The Picard-Lefschetz theory offers a promising tool to solve the sign problem in QCD and other field theories with complex path-integral weight. In this paper the Lefschetz-thimble approach is examined in simple fermionic models which share some features with QCD. In zero-dimensional versions of the Gross-Neveu model and the Nambu-Jona-Lasinio model, we study the structure of Lefschetz thimbles and its variation across the chiral phase transition. We map out a phase diagram in the complex four-fermion coupling plane using a thimble decomposition of the path integral, and demonstrate an interesting link between anti-Stokes lines and Lee-Yang zeros. In the case of nonzero mass, it is shown that the approach to the chiral limit is singular because of intricate cancellation between competing thimbles, which implies the necessity to sum up multiple thimbles related by symmetry. We also consider a Chern-Simons theory with fermions in 0 + 1-dimension and show how Lefschetz thimbles solve the complex phase problem caused by a topological term. These prototypical examples would aid future application of this framework to bona fide QCD.}, number={3}, journal={J. High Energ. Phys.}, publisher={Springer Science \mathplus Business Media}, author={Kanazawa, Takuya and Tanizaki, Yuya}, year={2015}, pages={044} }
@phdthesis{tanizaki_2015, title={Study on sign problem via Lefschetz-thimble path integral}, url={http://inspirehep.net/record/1635474}, DOI={10.15083/00073296}, school={Tokyo U.}, author={Tanizaki, Yuya}, year={2015}, month={Dec} }
@article{tanizaki_2014, title={Fermionic functional renormalization group approach to Bose-Einstein condensation of dimers}, volume={2014}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84898490553&partnerID=MN8TOARS}, DOI={10.1093/ptep/ptu009}, abstractNote={Fermionic functional renormalization group (f-FRG) is applied to describe Bose-Einstein condensation (BEC) of dimers for a two-component fermionic system with attractive contact interaction. In order to describe the system of dimers without introducing auxiliary bosonic fields (bosonization), we propose a new exact evolution-equation of the effective action in f-FRG with an infrared regulator for the fermion vertex. Then we analyze its basic properties in details. We show explicitly that the critical temperature of the free Bose gas is obtained naturally by this method without bosonization. Methods to make systematic improvement from the deep BEC limit are briefly discussed.}, number={2}, journal={PTEP}, author={Tanizaki, Yuya}, year={2014}, pages={023A04} }
@article{tanizaki_fejős_hatsuda_2014, title={Fermionic functional renormalization group approach to superfluid phase transition}, volume={2014}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84898483737&partnerID=MN8TOARS}, DOI={10.1093/ptep/ptu035}, abstractNote={Fermionic functional renormalization group (FRG) is applied to describe the superfluid phase transition of the two-component fermionic system with attractive contact interaction. Connection between the fermionic FRG approach and the conventional Bardeen-Cooper-Schrieffer (BCS) theory with Gorkov and Melik-Barkhudarov (GMB) correction are clarified in details in the weak coupling region by using the renormalization group flow of the fermionic four-point vertex with particle-particle and particle-hole scattering contributions. To go beyond the BCS+GMB theory, coupled FRG flow equations of the fermion self-energy and the four-point vertex are studied under an Ansatz concerning their frequency/momentum dependence. We found that the fermion self-energy turns out to be substantial even in the weak couping region, and the frequency dependence of the four-point vertex is essential to obtain the correct asymptotic-ultraviolet behavior of the flow for the self-energy. The superfluid transition temperature and the associated chemical potential are calculated in the region of negative scattering lengths.}, number={4}, journal={PTEP}, author={Tanizaki, Yuya and Fejős, Gergely and Hatsuda, Tetsuo}, year={2014}, pages={043I01} }
@inproceedings{tanizaki_fejős_hatsuda_2014, title={Functional renormalization group approach to conventional theory of superfluidity and beyond}, volume={529}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84906690155&partnerID=MN8TOARS}, DOI={10.1088/1742-6596/529/1/012027}, abstractNote={Fermionic functional renormalization group (FRG) is applied to describe the superfluid phase transition of the two-component fermionic system with attractive contact interaction. Connection between the fermionic FRG approach and the Bardeen-Cooper- Schrieffer (BCS) theory with its Gorkov and Melik-Barkhudarov (GMB) correction is made clear, and the FRG flow of the fermion self-energy is also studied to go beyond the BCS+GMB theory. The superfluid transition temperature and the associated chemical potential are calculated in the region of the negative scattering length using fermionic FRG.}, number={1}, booktitle={Journal of Physics: Conference Series}, author={Tanizaki, Yuya and Fejős, Gergely and Hatsuda, Tetsuo}, year={2014}, pages={012027} }
@inproceedings{tanizaki_2014, title={Many-Body Composite Bosons from the Viewpoint of Functional Renormalization}, volume={41}, url={http://inspirehep.net/record/1337529}, number={2}, booktitle={Bulg.J.Phys.}, author={Tanizaki, Yuya}, year={2014}, pages={180–186} }
@inproceedings{many-body composite bosons from the viewpoint of functional renormalization_2014, url={http://www.bjp-bg.com/paper.php?id=698}, booktitle={Bulgarian Journal of Physics}, year={2014}, month={Oct} }
@article{kashiwa_tanizaki_2014, title={Phase structure of SU (3) gauge-Higgs unification models at finite temperature}, volume={89}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84903692266&partnerID=MN8TOARS}, DOI={10.1103/PhysRevD.89.116013}, abstractNote={Five-dimensional $SU(3)$ gauge-Higgs unification models are studied at finite temperature in the warped extra dimension $S^1/\mathbb{Z}_2$. In order to investigate the phase structure, we developed a technique to compute the one-loop effective potential with the nontrivial Polyakov loop phase and with the nontrivial Wilson line phase along the extra dimension. Effective potentials as functions of two gauge-field condensations are shown for several simple matter contents, including fundamental, sextet, and adjoint representational Dirac fermions. Possible extensions and applications of our formalism are also briefly discussed.}, number={11}, journal={Phys.Rev.D}, author={Kashiwa, Kouji and Tanizaki, Yuya}, year={2014}, pages={116013} }
@article{tanizaki_koike_2014, title={Real-time path integral with Picard-Lefschetz theory and its applications to quantum tunneling}, volume={351}, url={http://dx.doi.org/10.1016/j.aop.2014.09.003}, DOI={10.1016/j.aop.2014.09.003}, abstractNote={Picard–Lefschetz theory is applied to path integrals of quantum mechanics, in order to compute real-time dynamics directly. After discussing basic properties of real-time path integrals on Lefschetz thimbles, we demonstrate its computational method in a concrete way by solving three simple examples of quantum mechanics. It is applied to quantum mechanics of a double-well potential, and quantum tunneling is discussed. We identify all of the complex saddle points of the classical action, and their properties are discussed in detail. However a big theoretical difficulty turns out to appear in rewriting the original path integral into a sum of path integrals on Lefschetz thimbles. We discuss generality of that problem and mention its importance. Real-time tunneling processes are shown to be described by those complex saddle points, and thus semi-classical description of real-time quantum tunneling becomes possible on solid ground if we could solve that problem.}, journal={Annals of Physics}, author={Tanizaki, Yuya and Koike, Takayuki}, year={2014}, month={Sep}, pages={250–274} }
@article{tanizaki_2013, title={Flow equation of functional renormalization group for three-body scattering problems}, volume={2013}, url={http://inspirehep.net/record/1227948}, DOI={10.1093/ptep/ptt092}, abstractNote={Functional renormalization group (FRG) is applied to the three-body scattering problem in the two-component fermionic system with an attractive contact interaction. We establish a new and correct flow equation on the basis of FRG and show that our flow equation is consistent with integral equations obtained from the Dyson-Schwinger equation. In particular, the relation of our flow equation and the Skornyakov and Ter-Martirosyan equation for the atom-dimer scattering is made clear.}, number={11}, journal={Progress of Theoretical and Experimental Physics}, author={Tanizaki, Yuya}, year={2013}, month={Nov}, pages={113A01} }